The Cohen-Macaulay Auslander algebras of string algebras

2023/03/12 by Liu, Yu-Zhe, Zhang, Chao
#FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2303.06645

Abstract

The Cohen-Macaulay Auslander algebra of any string algebra is explicitly constructed in this paper. Furthermore, we show that a class of special string algebras, which are called to be string algebras with G-condition, are representation-finite if and only if their Cohen-Macaulay Auslander algebras are representation-finite. Finally, the self-injective dimension of gentle algebras is characterized using their Cohen-Macaulay Auslander algebras.

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